I bent the plastic for the sides of the head the same way you are doing it. I can't see how the part of plastic that is covered can warp with the heat. Try heating it less, use different plastic or covering it in a cold damp cloth before adding the board.
As for cutting it to size. I made a template out of card. Draw around it and cut it with scissors, saw and knife. Clean up with a file and sandpaper.
To be honest, it sounds like you are worrying too much about how to do things. Thinking about doing some of this stuff can dive you around the bend. You just have to get on with doing it. If something turns out wrong, do it again another way.
Keith.